Taxpayers who go to a treasury office to pay their contributions complain that they wait more than 7 minutes, so there is a project to open a new box with an average cost of $80,000. The administrator...

Taxpayers who go to a treasury office to pay their contributions complain that they wait more than 7 minutes, so there is a project to open a new box with an average cost of $80,000. The administrator decides to analyze this situation and for this he takes a sample of 14 people, analyzes only one person per day. His analysis consists of measuring the fifth taxpayer who arrives in line and takes the time they wait to go to one of the two current boxes. The times taken are: 4.7, 5.8, 2.0, 6.1, 5.8, 4.7 5.7, 9.4, 5.1, 4.2, 5.9, 8.7, 2.7, 4.8. The administrator wishes to estimate a 95% confidence interval for the mean waiting time of taxpayers, which will allow him to determine whether or not to invest in a new box.
a). Determine the mean
b). Determine the standard deviation
c). Determine the confidence interval